RANGE-FINDERS. 
213 
representing the line of direct vision, and the dotted lines from Q to 
B the course of a reflected ray from the object Q, which on arriving at 
the face AB is bent towards a normal at that point through an angle 
of about 1J° (this being the “ refractive index ” for crown glass), and 
again in the opposite direction on issuing from the face AC. 
The figure represents the prism in use at the left end of the base; 
eye at B, the other observer at P, and the distant object at Q. If 
used at the right end of the base it must be turned upside down. 
It is possible to make a prism with equal base angles to do the same 
work from either end of the base without reversing; but in this case 
the apex angle must be about 90J°, and each base angle about 44J°. 
The angles reflected by such a prism, however, vary considerably, 
according to the way it is held—a defect which renders the instrument 
worthless for range-finding purposes, unless used in conjunction with 
a telescope to guide the eye in the true direction through the prism. 
Again, in describing the duplex mirror arrangement, Major Richardson 
observes, “ The mirrors are inclined to one another at an angle of 
88° 34' 3"P Such an instrument, if it reflected any angle at all, 
would reflect an angle of 177° 8' 6"; but, as a matter of fact, no 
reflection at all would be seen, because the observer’s head would be 
in the way. The proper arrangement would be to incline the mirrors 
at an angle of 44° 17' 1*5" to each other; as it is a well-known rule, 
founded on the principle of the sextant, that the angle observed is 
always double the angle between the faces of the mirrors. 
No instrument maker would undertake to grind and finish a prism 
to an accuracy of 1" for 30s., though he might offer fco do so for £30. 
It may be worth while to examine into the possibility of such an 
achievement. Take a prism (Fig. 3) having a side AB 1 in. long. 
Kff. 3. 
From centre A, radius AB , describe a short arc BC. If the angle 
BAC is 1", then the length of the circular arc BC will be *0000048 in. 
In other words, a difference of 1" in the angle of the prism would 
represent a difference of T q oiio-oo of an inch at the corners. At least 
five times this amount is taken off each time the faces are polished, so 
the difficulty of attaining such accuracy is apparent. 
Looking at it from another point of view, the length of a circular 
arc of 1" at a range of 5000 yds. is only *864 ins., or about the 
thickness of a man’s finger, and it would require an uncommonly 
powerful astronomical telescope to enable an observer to distinguish 
one side of a man’s finger from the other at such a range. Indeed, at 
